We develop a panel count model with a latent spatio‐temporal heterogeneous state process for monthly severe crimes at the census‐tract level in Pittsburgh, Pennsylvania. Our dataset combines Uniform Crime Reporting data with socio‐economic data. The likelihood is estimated by efficient importance sampling techniques for high‐dimensional spatial models. Estimation results confirm the broken‐windows hypothesis whereby less severe crimes are leading indicators for severe crimes. In addition to ML parameter estimates, we compute several other statistics of interest for law enforcement such as spatio‐temporal elasticities of severe crimes with respect to less severe crimes, out‐of‐sample forecasts, predictive distributions and validation test statistics. Copyright © 2016 John Wiley & Sons, Ltd.